Problem: Simplify the following expression: $a = \dfrac{n}{3} - \dfrac{8n}{5}$
Answer: In order to subtract expressions, they must have a common denominator. The smallest common denominator is the least common multiple of $3$ and $5$ $\lcm(3, 5) = 15$ $ a = \dfrac{5}{5} \cdot \dfrac{n}{3} - \dfrac{3}{3} \cdot \dfrac{8n}{5} $ $a = \dfrac{5n}{15} - \dfrac{24n}{15}$ $a = \dfrac{5n -24n}{15}$ $a = \dfrac{-19n}{15}$